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Equation in tau

Source: 2019 AIME I #9

March 14, 2019
2019 AIME IAIMEAIME Inumber theory

Problem Statement

Let τ(n)\tau (n) denote the number of positive integer divisors of nn. Find the sum of the six least positive integers nn that are solutions to τ(n)+τ(n+1)=7\tau (n) + \tau (n+1) = 7.
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